Many people believe that the average number of Facebook frie

Many people believe that the average number of Facebook friends is 130. The population standard deviation is 38.2. A random sample of 50 high school students in a particular county revealed that the average number of Facebook friends was 162. At a= 0.05, is there sufficient evidence to conclude that the mean number of friends is greater than 130?

1. State hypotheses by filling in the symbol (=,<,>, or not equal) and the population mean:

2. Critical z value is:

3. Z test value is:

4. Reject the null or do not reject the null:

5. Conclusion: is or is not enough evidence

Solution

1.

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   130  
Ha:    u   >   130   [ANSWER]

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2.
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    +   1.644853627   [ANSWER]

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3.  
              
Getting the test statistic, as              
              
X = sample mean =    162          
uo = hypothesized mean =    130          
n = sample size =    50          
s = standard deviation =    38.2          
              
Thus, z = (X - uo) * sqrt(n) / s =    5.923407591 [ANSWER]

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4.

As |z| > 1.6449, we REJECT THE NULL HYPOTHESIS. [ANSWER]

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5.          
              
Thus, there IS ENOUGH EVIDENCE to conclude that the mean number of friends is greater than 130. [CONCLUSION]